# Control Systems Engineering : Masons Gain

• BartlebyS
In summary, the conversation revolved around a system and equations related to steady state error and Mason's gain formula. The individual faced confusion while trying to draw a block diagram and apply Mason's gain formula. They were advised to correct their equations and block diagram, which ultimately led to a better understanding of signal flow graphs and Mason's formula.
BartlebyS

## Homework Statement

Here is the system I am looking at

## Homework Equations

So I worked out a formula for the steady state error and put it in a form similar to masons gain formula

## The Attempt at a Solution

But when I try and draw a block diagram and work out e I get confused by forward path and loop gain. It's not a question I have been asked, I am just playing, perhaps I cannot apply masons gain to my drawing? Or my drawing is wrong?

Your equations are not correct. For one thing, they are not dimensionally consistent: dh/dt = qin - qout has different dimensions on each side. q has dimension L^3 whereas dh/dt has dimension LT^(-1). L = length, T = time.

Your block diagram is good up to the point qin but then falls apart. Correct your equation for dh/dt: h cannot = qin - qout, you've already written dh/dt = qin - qout (which was incorrect also).

What is the correct relationship between dh/dt and qin - qout? (Hint: area of the bottom of the tank is a factor). And, once you get dh/dt right, how does one go from dh/dt to h?

Thanks for pointing that out, so I came to the idea that

a*dh/dt = dv/dt = q_in(t) - q_out(t) = 0 for steady state

which would make the rest of the derivation ok I hope?

Which then gave me a different drawing for the block diagram.

Which gives me a loop gain of (c_1 - c_2)/as

Instead of the c_1 / c_2 i got when I used the assumption that dv/dt = 0 for steady state. Am I still wrong with my equations or drawing?

I thought I had it for a minute there! Thanks for your help. I don't need to do it, it's just bugging me as I cannot relate it to the rest of my notes.

Your block diagram is now correct.

Loop gain = H(s)/H0(s).

Thanks again mate, I played with it some more, got the answers I wanted and have a much better understanding of signal flow graphs and masons formula.

## 1) What is the purpose of control systems engineering?

The purpose of control systems engineering is to design and implement systems that can automatically control and regulate the behavior of a physical system in order to achieve a desired output or performance. This involves the use of mathematical models, algorithms, and sensors to monitor and adjust the system's behavior.

## 2) How do Masons Gain approach control systems engineering?

Masons Gain is a method of control systems engineering that uses a graphical approach to design and analyze control systems. It was developed by Richard C. Dorf and Robert H. Bishop and is based on the Mason's Gain formula, which relates the system's inputs, outputs, and feedback to determine its overall gain.

## 3) What is the difference between open-loop and closed-loop control systems?

Open-loop control systems use only the system's input to control the output, without any feedback or adjustment. Closed-loop control systems, on the other hand, use sensors to measure the output and provide feedback to adjust the input in order to achieve a desired output. Closed-loop systems are generally more accurate and stable, but also more complex.

## 4) What are some common applications of control systems engineering?

Control systems engineering has a wide range of applications, including industrial automation, robotics, aerospace and defense, automotive systems, and environmental control. It can also be used in household appliances, medical devices, and even in the control of biological systems.

## 5) What are the main challenges in control systems engineering?

Some of the main challenges in control systems engineering include dealing with uncertainty and disturbances in the system, optimizing control parameters, ensuring stability and robustness, and integrating different components and subsystems. Additionally, as technology advances, control systems engineers must also keep up with new methods and tools for designing and analyzing control systems.

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